We present an algorithm for polygonizing closed implicit surfaces, which produces meshes adapted to the local curvature of the surface. Our method is similar to, but NOT based on, Marching Triangles, in that we start from a point on the surface and develop a mesh from that point using a surface-tracking approach. In a marked departure from previous approaches, our meshes approximate the surface through heuristics relying on curvature. Furthermore, our method works completely on-the-fly, resolving cracks as it proceeds, without the need for any post-remeshing step to correct failures. We have tested the algorithm with three different representations of implicit surfaces, Variational, analytical and MPU, using non-trivial data sets, yielding results that illustrate the flexibility and scalability of our technique. Performance comparisons with variants of Marching Cubes show that our approach is capable of good accuracy and meshing quality without sacrificing computing resources.